In Smart Island (SI) systems, the operators of power distribution system usually utilize actual-time measurement information as the Advanced Metering Infrastructure (AMI) to have accurate, efficient, advanced control and monitoring. SI system can be vulnerable to complicated information integrity attacks such as False Data Injection Attack (FDIA) on some equipment including sensors and controllers, which can generate misleading operational decision in the system. Today, lack of detailed research in the evaluation of power system that links the FDIAs with system stability is felt, and it will be important for both assessment of the effect of cyber-attack and taking preventive protection measures. In this regards, time-frequency-based differential approach is proposed for SI cyber-attack detection according to non-stationary signal assessment. In this paper, non-stationary signal processing approach of Hilbert-Huang Transform (HHT) is performed for the FDIA detection in several case studies. Since various critical case studies with a small FDIA in data where accurate and efficient detection can be a challenge, the simulation results confirm the efficiency of HHT approach. In this research, the configuration of the SI test case is developed in the MATLAB software with several Distributed Generations (DGs). As a result, it is found that the HHT approach is completely efficient and reliable for FDIA detection target in AC-SI. The simulation results verify that the proposed model is able to achieve accuracy rate of 93.17%.